A disturbance rejection joint estimation method for a closed-loop system based on an adaptive observer

Abstract

The application discloses a kind of adaptive observer-based closed-loop system anti-interference joint estimation method, it belongs to adaptive estimation field.The application solves the problem that it is difficult to obtain the parameters, state and disturbance of controlled object in real time accurately in closed-loop feedback structure.The estimation method of the application does not need prior information of controlled system parameters and disturbance, only utilizes the input and output measurement data and controller information of system, decouples control input and noise, solves the biased estimation problem caused by noise correlation in closed-loop structure;It has robustness to unknown disturbance and noise, and the adaptive observer-based closed-loop system anti-interference joint estimation problem is constructed by using the technology of relatively prime decomposition, and the signal unrelated to measurement noise is used as the reference input described by the stable image of controlled system, then a closed-loop robust adaptive estimation mechanism is built, so as to realize unbiased estimation of unknown parameters, state and disturbance of system.The method of the application can be applied to closed-loop system anti-interference joint estimation.

Description

Technical Field

[0001] The present invention belongs to the field of adaptive estimation, and in particular relates to a closed-loop system anti-disturbance joint estimation method based on an adaptive observer. Background Art

[0002] Due to the safety and reliability requirements of complex industrial systems, many industrial processes operate under feedback control and require real-time monitoring of the dynamics of the controlled objects. Because complex industrial systems are often subject to unknown disturbances during operation, it is difficult to accurately obtain the parameters of the controlled objects and the dynamics of the disturbances. Furthermore, the noise present in the measured data can become correlated with the control input through the closed-loop feedback structure, resulting in poor control performance. Therefore, it is necessary to accurately estimate the parameters, states, and disturbances of the controlled objects in closed-loop systems containing unknown disturbances and noise. This poses a challenge to the development of adaptive unbiased estimation methods for complex industrial systems. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem that it is difficult to accurately obtain the parameters, state and disturbance of the controlled object in real time in a closed-loop feedback structure, and to propose a closed-loop system anti-disturbance joint estimation method based on an adaptive observer.

[0004] The technical solution adopted by the present invention to solve the above technical problems is: a closed-loop system interference rejection joint estimation method based on an adaptive observer, the method specifically comprising the following steps:

[0005] Step 1: According to the order n of the controlled object in the closed-loop system, the output dimension m and the observability index σ1, σ2, ..., σ m Construct parameter matrix A o 、C o and D m ;

[0006] Step 2: Set the observer gain L r11 , L r12 , L r21 , L r22 and L c Initialize the observer's estimated values ​​of the state variables of the controller and the controlled object in the closed-loop system Initialize the observer to estimate the unknown parameters of the state space expression of the controlled object in the standard form of Lumberg observable form. Initialize auxiliary variables V0, initialize the state variable x related to the reference input signal describing the stable image of the controlled object ωd，0 , initialize the error covariance matrix P0 of the parameters and disturbance estimates;

[0007] Step 3: Initialize the number of iterations k = 0;

[0008] Step 4: Measure the reference input signal ω of the closed-loop system at time k k Based on the observer implementation form, the controller is decomposed into left coprime and the k-time signal v that is independent of the noise under the influence of disturbance is calculated. ωd,k , signal v ωd,k It is the reference input signal describing the stable image of the controlled object;

[0009] Step 5: Measure the control input signal u at time k k and the output signal y k , use the controller parameter matrix to calculate the matrix M L and M D , and based on M L 、M D 、u k and y k Construct information matrix Q k and

[0010] Step 6: According to the signal v ωd，k and information matrix Calculate auxiliary variables and residuals

[0011] Step 7: According to the information matrix Q k , auxiliary variables and residuals Calculate V k+1 , and P k+1 ;

[0012] Step 8: Determine whether the iteration stop condition is reached;

[0013] If it is achieved, the final estimation result is obtained;

[0014] If not reached, set k = k + 1 and calculate x ωd,k Then, return to step 4.

[0015] The beneficial effects of the present invention are:

[0016] 1. The estimation method of the present invention does not require prior information on the parameters and disturbances of the controlled object, but only uses the input and output measurement data and controller information of the system, thus avoiding estimation errors caused by inaccurate parameters and disturbance dynamic assumptions;

[0017] 2. The estimation method of the present invention decouples the control input and noise, solving the biased estimation problem caused by noise correlation in the closed-loop structure;

[0018] 3. The estimation method of the present invention is robust to unknown disturbances and noise, has a low computational burden, and can be implemented online. By using coprime decomposition technology to construct a signal uncorrelated with measurement noise, the signal serves as a reference input for describing the stable image of the controlled object. This method then constructs a closed-loop robust adaptive estimation mechanism, enabling unbiased real-time estimation of unknown system parameters, states, and disturbances, thereby improving the controller's control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a closed-loop system anti-disturbance joint estimation method based on an adaptive observer proposed by the present invention;

[0020] Figure 2 This is a simulation result diagram of parameter estimation error under the closed-loop feedback structure;

[0021] Figure 3 This is a simulation result diagram of the state estimation error under the closed-loop feedback structure;

[0022] Figure 4 This is a simulation result diagram of the disturbance estimation error under the closed-loop feedback structure. DETAILED DESCRIPTION

[0023] Specific implementation method 1: Combination Figure 1 This embodiment describes a closed-loop system disturbance rejection joint estimation method based on an adaptive observer, the method specifically comprising the following steps:

[0024] Step 1: According to the order n, output dimension m and observability index σ1, σ2, ..., σ of the controlled object in the closed-loop system (referring to other objects in the closed-loop system except the controller, such as the actuator), m Construct parameter matrix A o 、C o and D m ;

[0025] Step 2: Set the observer gain L r11 , L r12 , L r21 , L r22 and L c Initialize the observer's estimated values ​​of the state variables of the controller and the controlled object in the closed-loop system Initialize the observer to estimate the unknown parameters of the state space expression of the controlled object in the standard form of Lumberg observable form. Initialize auxiliary variables V0, initialize state variables x related to the dynamic changes of the reference input signal described by the stable image of the controlled object ωd,0 , initialize the error covariance matrix P0 of the parameters and disturbance estimates;

[0026] Step 3: Initialize the number of iterations k = 0;

[0027] Step 4: Measure the reference input signal ω of the closed-loop system at time k k Based on the observer implementation form, the controller is decomposed into left coprime and the k-time signal v that is independent of the noise under the influence of disturbance is calculated. ωd,k , signal v ωd,k It is the reference input signal describing the stable image of the controlled object;

[0028] Step 5: Measure the control input signal u at time k k and the output signal y k , use the controller parameter matrix to calculate the matrix M L and M D , and based on M L 、M D 、u k and y k Construct information matrix Q k and

[0029] Step 6: According to the signal v ωd，k and information matrix Calculate auxiliary variables and residuals

[0030] Step 7: According to the information matrix Q k , auxiliary variables and residuals Calculate V k+1 , and P k+1 ;

[0031] Step 8: Determine whether the iteration stop condition is reached;

[0032] If it is achieved, the final estimation result is obtained;

[0033] If not reached, set k = k + 1 and calculate x ωd,k Then, return to step 4.

[0034] Specific embodiment 2: This embodiment differs from the specific embodiment 1 in that the parameter matrix A o for:

[0035] A o =diag(A o1 , A o2 ,…,A om )

[0036]

[0037] Among them, the submatrix Aoi The dimension is σ i ×σ i , whose lower left corner is a dimension (σ i -1)×(σ i -1) identity matrix;

[0038] The parameter matrix Co is:

[0039]

[0040] Among them, C o The dimension is m×n, that is, the parameter matrix C o The n columns are divided into m blocks, the last element of the i-th row in the i-th block is 1, and the other elements are all 0, n>m;

[0041] Parameter matrix D m satisfy:

[0042] vec(G oc )=D m θ g

[0043]

[0044] Among them, vec represents the column expansion of the matrix, are all unknown parameters in the output matrix C of the state space expression of the controlled object, G oc It is the parameter matrix obtained by decomposing the matrix C, C=(I+G oc ) -1 C o , the superscript -1 represents the inverse of the matrix, I represents the identity matrix, and the parameter matrix G oc is The lower triangular matrix is ​​built, T stands for transpose;

[0045]

[0046] Matrix G oc The dimension is m×m, that is, the matrix G oc The first element of the first column is 0, and the second to mth elements are Matrix G oc The first and second elements of the second column are 0, and the third to mth elements are By analogy, the matrix G oc The first m-1 elements of the m-1th column of are all 0, and the mth element is Matrix G oc The elements in the mth column of are all 0.

[0047] Other steps and parameters are the same as those in the first embodiment.

[0048] Specific embodiment 3: This embodiment is different from specific embodiment 1 or 2 in that the observer gain L c Satisfy: Using the observer gain L c The constructed matrix (A c -L c C c )'s eigenvalues ​​lie within the unit circle;

[0049] Among them, A c and C c are the system matrix and output matrix of the controller state space expression respectively;

[0050] Observer gain L r11 , L r12 , L r21 , L r22 Satisfy: Using the observer gain L r11 , L r12 , L r21 , L r22 Constructed matrix A or The eigenvalues ​​of lie within the unit circle;

[0051] Matrix A or for:

[0052]

[0053] Among them, n c is the order of the controller, R is a real number;

[0054] Initialize the observer's estimate of the state variables of the controller and the controlled object in the closed-loop system Initialize the vector consisting of the estimated values ​​of all unknown parameters of the state space expression of the controlled object in the standard form of the Lumberg observable form Initialize auxiliary variable V0=0, Initialize x ωd，0 =0, Initialize the error covariance matrix of the parameters and perturbation estimates P0>0, P0∈R N×N ;

[0055] Where N is the sum of the dimensions of all unknown parameters and lumped disturbances in the closed-loop system. It includes the state variables of the controller and the controlled object that can be observed in the standard state space expression; Includes all unknown items in the system matrix A, input matrix B, output matrix C and direct transfer matrix D; V0 is used to correct parameter, state and disturbance estimates.

[0056] vector Contains parameters and the lumped disturbance d s The estimated value at time k, where B o , D o , L o It is the parameter matrix formed by linear transformation of the parameter matrix A, B, C, D in the state space expression of the controlled object Lumberg observable standard form, D o =(I+G oc )D,L o =L(I+G oc ), the definition of matrix L satisfies the equation LC o =AA o , so L contains all unknown parameters in A. B o =B-LD o , It is an estimate of the unknown parameters in the output matrix C of the controlled object.

[0057] Other steps and parameters are the same as those in the first or second embodiment.

[0058] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the specific process of step 4 is as follows:

[0059]

[0060] Among them, D c is the controller parameter matrix, yes The lumped perturbation estimate in .

[0061] The other steps and parameters are the same as those in the first to third embodiments.

[0062] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the specific process of step 5 is as follows:

[0063] M L =B c -L c D c +L r11 -L r12 D c

[0064] M D =L r21 -L r22 D c

[0065]

[0066]

[0067] Among them, B c is the controller parameter matrix, represents the Kronecker product, the superscript T represents the transpose of the matrix, I is the identity matrix, yes Middle pair D o The estimated results, D o =(I+G oc )D, that is D is the direct transfer matrix, in, yes Middle to L o The estimated results, L o =L(I+G oc )D, that is L meets LC o =AA o , A is the system matrix, is an intermediate variable;

[0068]

[0069]

[0070] The other steps and parameters are the same as those in the first to fourth embodiments.

[0071] It should be noted that when k = 0, let calculate The parameters are and

[0072] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the specific process of step 6 is as follows:

[0073]

[0074]

[0075] The other steps and parameters are the same as those in the first to fifth embodiments.

[0076] Specific embodiment 7: This embodiment differs from any one of specific embodiments 1 to 6 in that the specific process of step 7 is as follows:

[0077] V k+1 =A or V k +Q k

[0078]

[0079]

[0080]

[0081] Among them, γ k is the intermediate variable, and R′ is the noise covariance matrix.

[0082] The other steps and parameters are the same as those in the first to sixth embodiments.

[0083] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the intermediate variable γ k for:

[0084]

[0085]

[0086] Where σ∈R N×N is a given positive definite matrix.

[0087] The other steps and parameters are the same as those in the first to seventh embodiments.

[0088] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that, in step 8, x ωd，k The calculation method is:

[0089]

[0090] Among them, B c and D c is the parameter matrix of the controller.

[0091] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0092] Specific embodiment 10: This embodiment differs from any one of specific embodiments 1 to 9 in that the iteration stopping condition satisfies the following (1) or (2):

[0093] (1) and converge; that is, compared to The change of each element in is less than the set threshold, and compared with The change of each element in is less than the set threshold;

[0094] (2) Reach the maximum number of iterations.

[0095] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0096] The effectiveness of the method of the present invention will be illustrated below in conjunction with specific experimental results.

[0097] The DC motor system is a dual closed-loop DC speed control system. The controlled system consists of a PWM converter and a DC motor. The system output variables are the motor load and motor speed. The closed-loop structure contains two proportional-integral controllers, which use the negative feedback of speed and current to regulate the motor dynamics. The two controllers are connected in series and can be regarded as a single controller. The parameter matrix A of its discrete state space expression is c , B c , C c , D c for:

[0098]

[0099] C c =[10.9349 -10.6615 0 0.0871], D c =[0.5885 16.5390]

[0100] Set the parameter matrices A, B, C, D, E, and F of the discrete state space expression of the controlled object to:

[0101]

[0102] B=[-0.2956 -0.4925 0.7881 0.0013 0.0128 0.0059] T

[0103]

[0104]

[0105] The reference input of the closed-loop system is set to a white noise signal with a variance of 1. The disturbance of the controlled object is selected as a superimposed sine wave signal:

[0106]

[0107] The sampling period is 0.005s. The output and measurement noise of the controlled object are both set to have a variance of 1×10 -6 The closed-loop system interference rejection joint estimation method based on the adaptive observer is disabled from 0s to 0.1s. At 0.1s, the algorithm is enabled for estimation, with the initial estimated values ​​set to 0. The observer gain and algorithm parameters are set as required.

[0108] Step 1: Construct the following parameter matrix based on the order of the controlled system (n=6), the output dimension (m=2) and the observability of the controlled system:

[0109] D m = 0

[0110] Step two, set observer gain L r11 , L r12 , L r21 , L r22 , so that the eigenvalues of A or are located in the unit circle:

[0111]

[0112]

[0113] Set L c , so that the eigenvalues of (A c -L c C c ) are located in the unit circle, and set the initial value:

[0114]

[0115]

[0116] V0=0∈R 11×22 , x ωd，0 =0∈R 5×1 , P0>0∈R 22×22

[0117] Step three, initialize the iteration number k=0;

[0118] Step four, measure the reference input signal ω k at time k of the closed-loop system, and calculate the signal v ωd，k independent of noise under the influence of disturbance based on the left prime decomposition of the controller in the form of the observer, the signal v ωd,k is the reference input signal described by the stable image of the controlled object;

[0119] The specific process of the step four is:

[0120]

[0121] Wherein, D c is the parameter matrix of the controller, is the lumped disturbance estimation value in .

[0122] Step five, measure the control input signal u k and the output signal y k at time k, and calculate the matrix M L and M D, and based on M L 、M D 、u k and y k Construct information matrix Q k and

[0123] The specific process of step five is:

[0124] M L =B c -L c D c +L r11 -L r12 D c

[0125] M D =L r21 -L r22 D c

[0126]

[0127]

[0128] Among them, B c is the controller parameter matrix, represents the Kronecker product, the superscript T represents the transpose of the matrix, I is the identity matrix, yes Middle pair D o The estimated results, D o =(I+G oc )D, that is D is the direct transfer matrix, in, yes Middle to L o The estimated results, L o =L(I+G oc )D, that is L meets LC o =AA o , A is the system matrix, is an intermediate variable;

[0129]

[0130]

[0131] Step 6: According to the signal v ωd，k and information matrix Calculate auxiliary variables and residuals

[0132] The specific process of the step six is as follows:

[0133]

[0134]

[0135] Step seven, constructing a residual generator, an auxiliary filter and a parameter and disturbance estimator, calculating V k , an auxiliary variable and a residual according to the information matrix Q k+1 , k+1 ;

[0136] The specific process of the step seven is as follows:

[0137] V k+1 = A or V k + Q k

[0138]

[0139]

[0140]

[0141] wherein γ k is an intermediate variable, R' is a noise covariance matrix, and R = 1 x 10 -4 I3;

[0142]

[0143]

[0144] wherein σ ∈ R N×N is a given positive definite matrix, σ = 1 x 10 -6 I 22 .

[0145] Step eight, judging whether an iteration stopping condition is reached, i.e. whether the following (1) or (2) is satisfied:

[0146] (1), and are all converged; i.e. compared with the change of each element in V , the change of each element in V is smaller than a set threshold value;

[0147] (2), a maximum iteration number is reached.

[0148] ​If it is achieved, the final estimation result is obtained. The simulation results of the estimation method of the present invention are as follows: Figure 2 、 Figure 3 and Figure 4 shown.

[0149] If it is not reached, set k = k + 1 and calculate x ωd，k Then return to step 4;

[0150]

[0151] Among them, B c and D c is the parameter matrix of the controller.

[0152] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A closed-loop system disturbance rejection joint estimation method based on an adaptive observer, characterized in that: The method specifically comprises the following steps: Step 1: According to the order n, output dimension m and observability index σ1, σ2,…, σ m Construct parameter matrix A o 、C o and D m ; Step 2: Set the observer gain L r11 , L r12 , L r21 , L r22 and L c Initialize the observer's estimated values ​​of the state variables of the controller and the controlled object in the closed-loop system Initialize the observer to estimate the unknown parameters of the state space expression of the controlled object in the standard form of Lumberg observable form. Initialize auxiliary variables V0 and initialize the state variable x related to the reference input signal describing the stable state of the controlled object. ωd,0 , initialize the error covariance matrix P0 of the parameters and disturbance estimates; Step 3: Initialize the number of iterations k = 0; Step 4: Measure the reference input signal ω of the closed-loop system at time k k Based on the observer implementation form, the controller is decomposed into left coprime and the k-time signal v that is independent of the noise under the influence of disturbance is calculated. ωd,k , signal v ωd,k It is the reference input signal describing the stable image of the controlled object; Step 5: Measure the control input signal u at time k k and the output signal y k , use the controller parameter matrix to calculate the matrix M L and M D , and based on M L 、M D 、u k and y k Construct information matrix Q k and Step 6: According to the signal v ωd,k and information matrix Calculate auxiliary variables and residuals Step 7: According to the information matrix Q k , auxiliary variables and residuals Calculate V k+1 , and P k+1 ; Step 8: Determine whether the iteration stop condition is reached; If it is achieved, the final estimation result is obtained; If not reached, set k = k + 1 and calculate x ωd,k Then, return to step 4.

2. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 1, characterized in that: The parameter matrix A o for: THE o =diag(A o1 ,THE o2 ,…,THE om ) Among them, the submatrix A oi The dimension is σ i ×σ i ; The parameter matrix C o for: Among them, C o The dimension is m×n; Parameter matrix D m satisfy: vec(G oc )=D m i g Among them, vec represents the column expansion of the matrix, are all unknown parameters in the output matrix C of the state space expression of the controlled object, G oc It is the parameter matrix obtained by decomposing the matrix C, C=(I+G oc ) -1 C o , the superscript -1 represents the inverse of the matrix, I represents the identity matrix, and the parameter matrix G oc is The lower triangular matrix is ​​built, T stands for transpose; 3. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 2, characterized in that: The observer gain L c Satisfy: Using the observer gain L c The constructed matrix (A c -L c C c )’s eigenvalues ​​lie within the unit circle; Among them, A c and C c are the system matrix and output matrix of the controller state space expression respectively; Observer gain L r11 , L r12 , L r21 , L r22 Satisfy: Using the observer gain L r11 , L r12 , L r21 , L r22 Constructed matrix A or The eigenvalues ​​of lie within the unit circle; Matrix A or for: Among them, n c is the order of the controller, R is a real number; Initialize the observer's estimate of the state variables of the controller and the controlled object in the closed-loop system Initialize the vector consisting of the estimated values ​​of all unknown parameters of the state space expression of the controlled object in the standard form of the Lumberg observable form Initialize auxiliary variable V0=0, Initialize x ωd,0 =0, Initialize the error covariance matrix of the parameters and perturbation estimates P0>0, P0∈R N×N ; Where N is the sum of the dimensions of all unknown parameters and lumped disturbances in the closed-loop system.

4. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 3, characterized in that: The specific process of step 4 is as follows: Among them, D c is the controller parameter matrix, yes The lumped perturbation estimate in .

5. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 4, characterized in that: The specific process of step five is: M L =B c -L c D c +L r11 -L r12 D c M D =L r21 -L r22 D c Among them, B c is the controller parameter matrix, represents the Kronecker product, the superscript T represents the transpose of the matrix, I is the identity matrix, yes Middle pair D o The estimated result is D is the direct transfer matrix, in, yes Middle to L o The estimated result is L meets LC o =AA o , A is the system matrix, is an intermediate variable; 。 6. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 5, characterized in that: The specific process of step six is ​​as follows: The superscript -1 represents the inverse of the matrix.

7. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 6, characterized in that: The specific process of step seven is as follows: V k+1 =A or V k +Q k Among them, γ k is the intermediate variable, and R′ is the noise covariance matrix.

8. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 7, characterized in that: The intermediate variable γ k for: Where σ∈R N×N is a given positive definite matrix.

9. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 8, characterized in that: In the step eight, x ωd,k The calculation method is: Among them, B c and D c is the parameter matrix of the controller.

10. The closed-loop system disturbance rejection joint estimation method based on adaptive observer according to claim 9, characterized in that: The iteration stopping condition is to satisfy the following (1) or (2): (1) and All converge; (2) Reach the maximum number of iterations.

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